Size analysis and magnetic structure of nickel nanoparticles

Article abstract of DOI:10.1016/j.jmmm.2010.07.046

The size distribution of an assembly of fcc nickel nanoparticles is studied by measuring the temperature dependent magnetization curves fitted by a uniform model and a coreshell model, both based on the Langevin function for superparamagnetism with a log-normal particle volume distribution. The uniform model fits lead to a spontaneous magnetization M_s much smaller than the M_s for bulk nickel and to particle sizes larger than the ones evaluated by transmission electron microscopy; the coreshell model fits can result in a correct size distribution but the M_s in the core becomes significantly greater than the M_s for bulk nickel. It is concluded that there is a coreshell magnetic structure in nickel particles. Although the enhanced M_s in the core may be related to the narrowing of the energy bands of 3d electrons in small fcc nickel particles, the modeling values of M_s are over large compared with previous calculations on nickel clusters of different structures, which implies possible existence of an exchange interaction between the core and the shell, which is not considered in the simple coreshell model.

Full text of DOI:10.1016/j.jmmm.2010.07.046

Journal of Magnetism and Magnetic Materials 322 (2010) 3834–3840
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials
journal homepage: www.elsevier.com/locate/jmmm
Size analysis and magnetic structure of nickel nanoparticles
Ã
D.-X. Chen a, , O. Pascu b, A. Roig b, A. Sanchez c
a
ꢀ
ICREA and Departament de F´ısica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Spain
b
c
ꢀ
Institut de Ciencia de Materials de Barcelona (ICMAB), CSIC, 08193 Bellaterra, Spain
ꢀ
Departament de F´ısica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Spain
a r t i c l e i n f o
a b s t r a c t
Article history:
The size distribution of an assembly of fcc nickel nanoparticles is studied by measuring the temperature
dependent magnetization curves fitted by a uniform model and a core–shell model, both based on the
Langevin function for superparamagnetism with a log-normal particle volume distribution. The uniform
model fits lead to a spontaneous magnetization Ms much smaller than the Ms for bulk nickel and to
particle sizes larger than the ones evaluated by transmission electron microscopy; the core–shell model
fits can result in a correct size distribution but the Ms in the core becomes significantly greater than the
Ms for bulk nickel. It is concluded that there is a core–shell magnetic structure in nickel particles.
Although the enhanced Ms in the core may be related to the narrowing of the energy bands of 3d
electrons in small fcc nickel particles, the modeling values of Ms are over large compared with previous
calculations on nickel clusters of different structures, which implies possible existence of an exchange
interaction between the core and the shell, which is not considered in the simple core–shell model.
& 2010 Elsevier B.V. All rights reserved.
Received 22 May 2010
Received in revised form
31 July 2010
Available online 7 August 2010
Keywords:
Magnetization curve
Metallic ferromagnetic nanoparticle
Particle size determination
Core–shell model
1. Introduction
respectively [6]. Thus, the particle moment may be determined by
magnetic measurements, from which the particle volume may be
obtained as m0/Ms if the saturation magnetization Ms is known.
The saturation magnetization of particles Ms was first thought
to be the same as for the bulk material that had the same
composition and structure as the particles. However, already in
Ferrimagnetic or ferromagnetic fine particles present rich
physical phenomena and also serve as a key element in many
technologies, including recent developments in fields such as
magnetic separation, drug delivery, hyperthermia treatments and
magnetic resonance imaging contrast agents [1], which have
followed earlier applications in magnetic recording and ferro-
magnetic liquids [2,3]. In most cases, a knowledge of size
distribution of the fine particles is crucially important for the
proper working of a particular application.
The magnetic particle size distribution of powder samples may
be determined from the measurements of magnetization curve
based on the theory of superparamagnetism, first proposed by
Bean and co-workers [4–6]. This theory defines a dilute assembly
of ferromagnetic particles as superparamagnetic if the particles
are single domain and when the thermal energy at the
temperature of the experiment is sufficient to equilibrate
the magnetization of the assembly in a time shorter than that of
the experiment. The reduced magnetization M(H) curve of the
superparamagnetic assembly is expressed by the Langevin
function
1968, Ms of many acicular
gꢀFe2O3 polycrystalline particles was
measured at room temperature, and it was found that Ms
decreased with decreasing the average crystallite size determined
from X-ray diffraction (XRD) line broadening measurements using
the Scherrer relation [7]. This phenomenon was explained by
assuming the crystallites to be separated by a nonmagnetic grain
shell on the order of 0.6 nm thick. A similar effect was found for
single-domain superparamagnetic Fe3O4 particles in ferromag-
netic liquids; their magnetization curve could be correlated to the
superparamagnetic theory only when the size distribution of the
suspended particles was considered with their volumetric con-
centration corrected for the formation of a nonmagnetic surface
mantle one-unit-cell thick [8]. Such surface mantle was later
called the magnetically dead layer with respect to the magnetic
core [9]. The differences in magnetic structure between the
surface layer and the core have been an interesting topic in
physics [10–13].
LðxÞ ¼ cothxꢀ1=x,
ð1Þ
A frequently adopted approach since then has been to assume
the particles with a certain size distribution to have the same Ms
as the bulk and to determine by magnetic measurements a
‘‘magnetic size’’, which is significantly smaller than the physical
size obtained from transmission electron microscopy (TEM) data.
In recent years, however, in the determination of particle sizes by
magnetic measurements, a paramagnetic susceptibility term has
where x ¼ m0m0H=kBT, with m0, kB, and T being the particle
magnetic moment, the Boltzmann constant, and temperature,
Ã
Corresponding author.
E-mail address: duxing.chen@uab.es (D.-X. Chen).
0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2010.07.046

D.-X. Chen et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3834–3840
3835
been incorporated to the superparamagnetic term, and the
magnetically determined sizes of Fe3O4 or
ꢀFe2O3 nanoparticles
g
are found to be in agreement with the sizes determined by TEM or
XRD techniques [14–16]. In [17], we have completed this
approach by proposing a core–shell model and a uniform model,
both based on the Langevin function with a log-normal particle
volume distribution, and by performing careful fits to experi-
mental data of iron-oxide nanoparticles. It has been found that
the core–shell model gives particle sizes consistent with the TEM
or XRD sizes, while the sizes determined by the uniform model
are larger with a wider distribution. The core–shell model has
been used for the size analysis of superparamagnetic iron-oxide
particles, which could be used potentially as contrast agents of
magnetic resonance imaging [18].
In this work, we will use the methodology developed in [17] to
study ferromagnetic nickel nanoparticles, to be compared with
experimental and theoretical results on similar particles already
published in the literature [19–29]. We will show that our
particles display interesting magnetic features different from
ferrimagnetic iron-oxide nanoparticles.
2. Experimental
2.1. Synthesis of nickel nanoparticles
Fig. 1. TEM image of studied nanoparticles. The inset is a selected area electron
Nickel nanoparticles were synthesized by thermal decomposi-
tion of a nickel organometallic precursor, adapting the method
reported in [27]. For the studied particles, 1 mmol of Ni(acac)2
was added to 7 ml oleylamine and 3 mmol trioctylphosphine, and
the mixture was heated to 130 1C and stirred magnetically under a
flow of high purity argon gas for 20 min, and then further heated
to 250 1C and maintained at this temperature for 30 min. After
cooling to room temperature, the nanoparticles were precipitated
by adding excessive ethanol, followed by centrifugation. The as-
prepared precipitate was dried at 70 1C overnight then weighted.
To prevent oxidation, the as-synthesized nickel nanoparticles
were kept as a concentrated dispersion in hexane of a known
concentration.
diffraction pattern with indexed planes.
3000
(111)
2500
2000
1500
(200)
1000
2.2. Characterization of nanoparticles
(220)
500
0
(311)
90
TEM and XRD were used for morphological and structural
characterization of the nanoparticles. TEM images were obtained
using a JEOL JEM-2011 electron microscope, operating at 200 kV.
40
50
60
70
80
The sample was prepared by depositing
a drop of dilute
2θ (degree)
nanoparticles hexane dispersion onto a TEM carbon grid followed
by room temperature drying. A representative TEM image is
shown in Fig. 1, where we see that most particles are roughly
spherical.
Fig. 2. The X-ray diffraction pattern of studied nanoparticles.
XRD was performed for
a
powder sample by
a Rigaku
2.3. Magnetic measurements
diffractometer with Cu K
a
incident radiation ð
l
¼ 0:154 nmÞ. The
resulting pattern is shown in Fig. 2, from which four peaks are
observed corresponding to the (1 1 1), (2 0 0), (2 2 0), and (3 1 1)
planes of fcc structure of lattice parameter 0.354 nm (very near
the standard value 0.352 nm for bulk nickel). The average
crystallite size may be determined from XRD pattern using
the Scherrer relation with a shape factor of 4/3 for spherical
particles [30]
The magnetic measurements were performed with a super-
conducting quantum interference device (SQUID) magnetometer,
which was carefully calibrated by using a Pd standard sample.
The nickel sample was powder packed in a plastic capsule. The
zero-field and field (3 kA/m) cooled measurements were carried
out for one sample during warming at a measuring applied field
Ha¼3 kA/m. The results are shown in Fig. 3, from which we see
that the external susceptibility M/Ha increases and then decreases
with increasing temperature T for the zero-field cooled case,
whereas it decreases monotonically with T for the field cooled
case and that both curves merge at T 475 K.
4k
l
DXRD
¼
,
ð2Þ
3D
ð2yÞcosy
where Scherrer constant k¼0.9, the peak is centered at 2
y
, and
Dð2yÞ (rad) is the width of the peak at half maximum intensity.
Another sample was prepared with more caution concerning
the powder mass (to get more accurate magnetization) and its
The DXRD determined from the (1 1 1), (2 0 0), (2 2 0), and (3 1 1)
peaks is 5.2, 3.4, 5.2, and 4.5 nm, respectively.

3836
D.-X. Chen et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3834–3840
hysteresis loop corresponding unphysically to a negative energy
loss, as shown in Fig. 4. Such a loop is corrected to a reversible one
after shift determined by the calibration of the SQUID
8
6
4
2
0
a
magnetometer with a paramagnetic Pd standard sample. This
Zero-field cooled
Field cooled
correction is essential at low jHaj only.
Moreover,
a demagnetizing correction was performed to
convert the applied field Ha to the internal field H in the sample
by using
H ¼ HaꢀNmM,
ð3Þ
where magnetometric demagnetizing factor Nm¼0.02 was taken
(see below) [32]. After such corrections, the 0M vs 0H loops are
m
m
plotted in Fig. 5 by solid (ascending branch) and open circles
(descending branch).
Μ/Ηa measured with increasing T at Ha = 3 kA/m
For calculating magnetization, the mass fraction (1ꢀfm) of
surfactants on the surface of dried nanoparticles was obtained
by thermogravimetric analysis (TGA). A powder sample of about
10-mg mass was measured with a Mettler Toledo TGA/SDTA 851
at heating rate 10 1C/min in a temperature range 30–800 1C under
flowing N2.
0
50
100
150
200
250
300
T (K)
Fig. 3. External susceptibility M/Ha of a powder sample measured at Ha¼3 kA/m
as a function of increasing temperature T, after cooling at Ha¼0 and 3 kA/m.
The original data given by the magnetometer were the
moment m of the sample in emu units. The formula to calculate
m
0M in SI units is m0M ¼ 4pmr=ð10 000wfmÞ, where fm¼0.83 is
obtained from TGA data and w and
r are the sample mass and the
density of nickel (8.9 g/cm3), respectively, in cgs units.
T = 100 K
0.06
0.04
0.02
0.00
a
Directly measured loop
Ascending branch after shift
Descending branch after shift
0.000
0.002
0.004
0.006
0.008
0.010
μ0Ha (T)
Fig. 4. The correction to M(Ha) loop obtained from SQUID magnetometric
measurements, showing how the unphysical measured loop (low-field portion)
is shifted to a reversible magnetization curve.
dispersion (to reduce demagnetizing effects) and used for the
measurements of magnetization loops at T¼100, 200, 300, and
400 K. In the data treatment, a shift of 70:00165 T was performed
for the ascending and descending applied field m0Ha to correct the
effects of remanence of the SQUID superconducting magnet, so
that the magnetic reversibility of the measured sample could be
accurately checked.
b
A comparison between the directly recorded and corrected
hysteresis loops in a low-field region is shown in Fig. 4. Owing to
the irreversible magnetization of the superconducting wire of
which the magnet of the SQUID magnetometer is wound, the field
at the magnet center is produced not only by the current flowing
through the wire, from which the field reading is calculated, but
also by the poles in the magnetized wire itself, which gives an
error in the field measurements. According to the critical-state
model [31], the magnetization of the wire will be along the field
produced by the transport current when the current decreases
from a large value as in our case. Thus, the poles will produce a
negative demagnetizing field at the magnet center when the total
field sweeps from a large positive value in the descending branch.
As a result, by cycling the field between 75 T, the directly
Fig. 5. The magnetization M versus field H loops (solid and open circles for
ascending and descending branches, respectively) of a powder sample measured
at T¼100, 200, 300, and 400 K and their fits (lines) by the uniform model (a) and
the core–shell model (b). Arrows indicate the direction of increasing T.
measured M(Ha) of
a paramagnetic sample will become a

D.-X. Chen et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3834–3840
3837
3. Model fits to magnetization curves
3.1. Uniform and core–shell models
To fit the 0M versus 0H curves, we assume that all particles
are spherical without mutual interaction and the particle volume
v distribution by volume follows the log-normal probability
density function
3.2. Model fits
Using Eq. (6) to calculate numerically the magnetization curve
of the uniform model for given values of T, we fix the values of the
Boltzmann constant kB ¼ 1:38 ꢃ 10ꢀ23 J=K and the permeability of
m
m
free space m0 ¼ 4
p
ꢃ 10ꢀ7 H=m, and change the values of para-
meters ,D0,w, and Ms(T) iteratively until the measured m0M vs.
s
m
0H curves for T¼300 and 400 K are best fitted with a proper
demagnetizing correction of Nm¼0.02. Then, we fix the same data
for ,D0, and
and change Ms(T) for T¼100 and 200 K until the
low and high field portions of the measured 0M vs. 0H curves
"
#
1
ðlnvꢀm 2
Þ
s
w
pffiffiffiffiffiffi
pðv;
m
,
s
Þ ¼
exp ꢀ
,
ð4Þ
2
2s
m
m
2ps
v
are best fitted. All the four fitting curves are plotted as solid lines
in Fig. 5(a), with fitting parameters listed.
where
m
and
s
are the mean and the standard deviation of lnv. For
convenience, we define
For the core–shell model fits using Eq. (8), the values of Ms(T) are
set as four times those for the uniform model (as explained below),
and the fitting curves are plotted in Fig. 5(b), with all fitting
parameters listed. It should be noted that the data for T¼100 and
m
ꢁ lnv0 ¼ lnð
p
D30=6Þ,
ð5Þ
where v0 and D0 are the median volume and its corresponding
diameter, respectively.
The uniform model assumes all the particles to have the same
spontaneous magnetization Ms (equal to the average saturation
magnetization of the superparamagnetism for the entire particle
assembly) and the same paramagnetic susceptibility w. Magneti-
zation M as a function of field H is contributed by the super-
paramagnetism and paramagnetism of all the particles with a
200 K cannot be well fitted by using the same set of
those used for higher temperatures. Since
independent for the same assembly of particles and the effect of
small, this implies that at least should change with T and H if a
core–shell model is still applied. Physically, this may be
s
,D0,
and D0 should be T
is
d, and w as
s
w
d
a
consequence of the interaction occurring between the core and the
shell, which will be discussed in Section 4.6.
It is necessary to make an explanation on the demagnetizing
correction. In the measurements of our superparamagnetic powder,
the magnetic moment and the applied field are measured accurately
since the SQUID magnetometer has been properly calibrated and the
field error owing to the magnetization of the superconducting wire
has been corrected. However, there is still a demagnetizing effect to
be considered. This effect can be neglected when the magnetic
particles are very loosely packed, as in the case of [17], but it cannot in
most cases. We propose a way to determine Nm in the present work
by measuring M(H) curves at more than two different T values and
fitting them logically with the same set of parameters. It is shown
that the fitting can be well done only when Nm is incorporated as an
extra parameter, so that proper Nm is determined for the measured
sample. Our experience shows that Nm cannot be larger than 0.02.
Such a small Nm value comes from loosely packed particles in the
sample; Nm¼0.02 gives a rough estimate of the volume fraction of the
nickel particles in the sample, which is about 0.1 in the present case.
It is important to mention that such a demagnetizing correction
was not performed in most works on magnetic properties of
assemblies of magnetic fine particles, so that low-field super-
paramagnetic susceptibility w0 obeying the Curie law was modified
to one obeying the Curie–Weiss law. In our case, the Curie law may
volume distribution pðv;
m
,
s
Þ and is expressed by
Z
1
MðHÞ ¼
pðv;
m,
sÞ½MsLðxÞþ
wHꢂ dv,
ð6Þ
ð7Þ
0
where L(x) is expressed by Eq. (1) with
x ¼ m0MsvH=kBT:
The core–shell model assumes that each particle has an inner
single-domain core with spontaneous magnetization Ms and an
outer paramagnetic shell of susceptibility
particle diameter D42 . Writing the volumes of a particle, its
core, and its shell as v, vc, and vs, respectively, we have in general
w and thickness d, if the
d
3
v ¼ vc þvs ¼ p d and vc ¼ pðDꢀ2dÞ =6
D3=6 and vc¼0 if Do2
otherwise. Thus, M(H) is contributed by the core superparamag-
netism and the shell paramagnetism of all the particles with a
volume distribution pðv;
m,
sÞ and is expressed by
Z
1
MðHÞ ¼
pðv;
m,
s
Þvꢀ1½MsvcLðxÞþvs
wHꢂ dv,
ð8Þ
ð9Þ
0
where L(x) is expressed by Eq. (1) with
be expressed by m20Ms2=
m0Ms in particles is given in Fig. 5(a) and w0 may be obtained from
the experimental M/H at
w0pT [17], where the average values of
x ¼ m0MsvcH=kBT:
m
0H ꢄ 0:004 T. A comparison of m20Ms2=w0
vs. T before and after demagnetizing correction is shown in Fig. 6.
We see that the Curie–Weiss relation m20Ms2=w0pðTꢀTcÞ with Tc o0
is changed into the Curie relation by the demagnetizing correction.
These uniform and core–shell models have been explained in
greater detail in [17]. Most researchers used the Langevin function
to fit superparamagnetic magnetization curves of particle systems
without considering a paramagnetic contribution (i.e.,
w ¼ 0) and
3.3. Size distribution
a magnetic core–shell structure. Although such model fits cannot
be good according to our experience, we will call the model used
in, for example, [24,26] without explicitly mentioning a core–shell
structure as a uniform model for simplicity. Our core–shell model
is a completion of some previous models where a core–shell
structure was considered, and essentially different from a popular
model by which the problem was treated self-inconsistently
leading to a magnetic size even smaller than the size of the core,
as already discussed in [17]. Moreover, our core–shell structure is
a magnetic one that may not be seen morphologically, which is
different from cases where the core and shell are made of
different materials [20,28].
The log-normal probability density function pðv;
m,sÞ of the
particle volume distribution by volume, expressed by Eq. (4), may
be converted into the probability density function of the particle
diameter distribution by volume,
"
#
2
3
9ðlnDꢀlnD0Þ
pffiffiffiffiffiffi
pðDÞ ¼
exp ꢀ
,
ð10Þ
ð11Þ
2
2s
2ps
D
where particle diameter
D ¼ ð6v=p 1=3
Þ
:

3838
D.-X. Chen et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3834–3840
using the Scherrer relation is the particle-volume-weighted
average diameter [17]
0.04
0.03
0.02
0.01
0.00
Z
1
Dvd
¼
pðv;
m,
sÞDðvÞ dv:
ð12Þ
0
Dvd¼8.9 nm is calculated using D0¼8.8 nm and
s
¼ 0:4 for the
core–shell model fits, which is consistent with TEM observation.
This Dvd is roughly twice the average DRXD¼4.6 nm for the
crystallites, so that the nickel particles shown in the TEM images
are polycrystalline in general. This is different from the case of
ferrimagnetic iron-oxide particles, whose particles observed in
TEM are single crystals [17,18].
Before demag. correction
After demag. correction
Since DXRD determined from the (2 0 0) peak is significantly
smaller than that determined from the (1 1 1) peak, the crystal-
lites seem to have a cube-like shape.
0
50
100 150 200 250 300 350 400
T (K)
Fig. 6. Influence of demagnetizing correction on Ms2=
w0 vs. T relation. The solid and
dashed lines show the linear relations of the Curie and the Curie–Weiss laws,
4.2. Superparamagnetism
respectively.
As shown in Fig. 5, there is no hysteresis occurring in the
magnetization loops for T between 100 and 400 K, i.e., the thermal
energy is sufficient to equilibrate the magnetization at each field
value in the time of experiment, so that the assembly of the
studied nickel nanoparticles may be superparamagnetic in this T
range. Being polycrystalline, each particle is a single magnetic
0.4
From uniform model
From core-shell model
0.3
domain, since after
a proper demagnetizing correction, the
From TEM observation
measured magnetization curves at T¼300 and 400 K can be well
fitted by the uniform model of superparamagnetism with the
same set of parameters. However, to further confirm the super-
paramagnetism, the magnetization curves at lower T should also
From core-shell model
with bulk-Ni Ms (300 K)
0.2
0.1
0.0
be well fitted with the same set of D0 and
of the particles should not be T dependent, and both D0 and
s values, since the sizes
s
parameters should define a size distribution that is consistent
with the one determined by TEM measurements. These two
requirements may be fulfilled by using the core–shell model fits,
as discussed below.
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18
D (nm)
4.3. Model fits and particle sizes
The uniform model fits lead to over-large D0 and
s, which
Fig. 7. Particle size distribution by volume obtained from magnetization curve fits
by the uniform (solid line) and core–shell models (dashed line) and from TEM
images (open squares). The dotted line is obtained from the core–shell model fit at
T¼300 K with m0Ms ¼ 0:607 T, the value of bulk nickel.
results in a wider particle size distribution centered at a larger D
compared with the TEM size distribution (Fig. 7). As shown in
[17], the same magnetization curve may be equally well fitted by
either the uniform model or the core–shell model, and the D0 and
s
obtained by the core–shell model fitting are smaller than those
obtained by the uniform model fitting. Increasing the shell
thickness and the Ms in the core to fit the magnetization curves
The p(D) vs D curves calculated from D0¼9.6 nm and
for the uniform model fits and from D0¼8.8 nm and
s
¼ 0:48
s
¼ 0:4 for
d
the core–shell model fits are plotted in Fig. 7 by solid and dashed
lines, respectively. We see that the former distribution is wider
than the latter with its maximum located at larger D. The square
symbols are the size distribution by volume evaluated by
measuring more than 550 nanoparticles from the TEM image in
Fig. 1; it shows a good coincidence with the dashed line. In fact,
the fitting parameters of the core–shell model have been chosen
iteratively by comparing the modeling distribution curve with the
TEM results.
by the core–shell model, we find a set of parameters listed in
Fig. 5(b) that are best in agreement with the TEM data.
The advantage of the core–shell model over the uniform model
is not shown by a better fitting quality to the M(H) curves but by
the obtained size distribution to be closer to the TEM data. In
principle, an increase in Ms could be compensated by a decrease in
vc to maintain constant Msvc in Eq. (9), so that a size distribution
that is most close to the TEM one may be obtained by changing
both freely. However, in order to maintain the same distribution
of Msvc, the increase in Ms and decrease in vc have to be realized
by increasing
reason for D0 and
d
and decreasing D0 and
s simultaneously. The
4. Discussion
s
determined from the core–shell model fits to
be smaller than those from the uniform model can be understood
as follows. In the core–shell model, the contribution of the shell of
a certain thickness to superparamagnetism is removed, and the
shell occupies a larger volume fraction in smaller particles than in
larger particles. As a result, the total particle size distribution with
4.1. Polycrystalline nanoparticles
Since the X-ray intensity is proportional to the total particle
volume and the peak width is directly related to the particle size,
the particle diameter determined directly from XRD patterns
smaller D0 and
s obtained by the core–shell model fits will give

D.-X. Chen et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3834–3840
3839
practically the same Msvc distribution as that obtained by uniform
model fits with larger D0 and s.
enhancement in Ms occurs only in the core, and they should
require that the exchange effects be weakened (or even change
the sign to antiferromagnetic coupling) near the particle surface,
leading to a very small Ms in the shell. As to the paramagnetism, it
should be Pauli paramagnetism resulting from the band structure,
4.4. Magnetic structure
so that
w is approximately temperature independent [34].
The goodness of the core–shell model fits indicates the
existence of
nanoparticles.
a core–shell magnetic structure in the nickel
4.5. Comparison with previous works
Different from the case of ferrimagnetic iron oxide, for which
the Ms in the core is the same as that for the bulk, the Ms in the
core of nickel nanoparticles can be greater than its bulk value. The
m0MsðTÞ data points resulting from the uniform and core–shell
model fits are drawn in Fig. 8, where, for comparison, a solid curve
is plotted for bulk nickel, calculated from
The temperature dependence of Ms shown in Fig. 8 deduced
from the core–shell model fits is qualitatively similar to that
found in [26], where magnetization of nickel nanoparticles of
average diameter 3 nm was detected by Kerr ellipticity at
T 4300 K, and explained by quantum Monte-Carlo simulations
considering Ising spins in a nanocube [22]. However, fitting the
experimental M(H,T) by a uniform model without considering a
size distribution, the authors of [26] obtained a spontaneous
magnetic moment per ion to be 2:5mB per atom, which is a value
10 times larger than our result without physical basis.
Ms of nickel particles was found to decrease quickly with
decreasing particle size in [19], which is consistent with our
results. By Langevin function fitting with a uniform model in [24],
Ms of nickel nanoparticles of TEM size about 3.3 nm was found
approximately the same as that of bulk nickel with ‘‘magnetic’’
size about 5 nm. This seems to be consistent with our results,
since the disagreement between the two sizes could be resolved
by a core–shell model fit to get Ms in the core much larger than Ms
of bulk nickel. Ms of nickel nanoparticles in silica gel was found to
be about 90% of Ms of bulk nickel for particle sizes between 3 and
10 nm in [20]. This would help to understand the magnetic
structure in nickel particles by showing significant influence of
silica gel if it is further confirmed.
3=2
5=2
1=3
MsðTÞ ¼ Msð0Þ½1ꢀ0:15ðT=TcÞ ꢀ0:85ðT=TcÞ
ꢂ
,
ð13Þ
where Ms(0)¼0.65 T and Tc¼630 K [33], and the dashed and
dotted curves are drawn artificially for the uniform and core–shell
model results to have the same Tc as the bulk. We see that
although the Ms for the uniform model is always much smaller
than that for the bulk, the Ms in the core could be significantly
larger.
This difference in magnetic structure between ferromagnetic
and ferrimagnetic nanoparticles suggests the difference in the
nature of magnetic ordering. As described in [34], the magnetic
ordering in ferrimagnetic iron oxides results from the local
superexchange interaction between the 3d electrons of iron ions
with certain magnetic moments through the oxygen ions in
between, and when the surface effects reduce the interaction so
that Ms becomes zero in a surface layer, Ms in the core remains its
bulk value. The detailed mechanisms for the zero Ms in the surface
layer were studied in [10–13].
For ferromagnets, however, Ms(0) comes from the 3d electrons
itinerant among the atoms, so that the discrete energy levels for
isolated atoms are extended to certain spin-up and spin-down
energy bands splitted by exchange field. Since both bands are
partially overlapped in energy, so that the spontaneous magnetic
moment per ion, given by the difference in the number of
In a study of nickel nanoparticles [28], a synthesis procedure
similar to ours was adopted with polycrystalline fcc grains
obtained. Since the high-field magnetization was found to be,
similarly to our case, significantly smaller than that for bulk
nickel, the existence of an amorphous antiferromagnetic NiO shell
was assumed. The shell thickness was estimated to be around
1 nm by assuming the bulk-nickel Ms value in the core and using
the densities for bulk nickel and bulk NiO in the core and the shell,
respectively. Different from that approach, we have assumed the
particles are pure nickel and determined the shell thickness by
careful uniform and core–shell model fits to the entire magneti-
electrons in the spin-up and the spin-down bands, is about 0:6mB
which is much smaller than 2mB
,
ð
m0Ms ꢄ 2:1 TÞ, expected by 2
vacancies in the 3d shell of nickel atom [34]. For a nano-sized
particle, the spin-up and spin-down bands should be energetically
narrower than those for the bulk with less overlap in the same
exchange field, so that m0Msð0Þ being between 0.65 and 2.1 T may
be expected. The core–shell model fits indicate that such an
zation curves with the same set of D0 and
s parameters at
different temperatures, and comparing the resulting size
distribution with TEM measurements, so that the thicker shell is
found with the Ms in the core to be greater than that for the bulk
nickel. We should emphasize that using the bulk-nickel Ms for the
core, not only the core–shell model fit gives overlarge D0 and
s,
but the resultant D0 and are also unphysically T dependent. As
s
an example, we show the size distribution curve (dotted line)
obtained by the core–shell model fit at T¼300 K with
m0Ms ¼ 0:607 T in Fig. 7.
4.6. Possible exchange interaction between the core and the shell
The Ms in the core resultant from the core–shell model fits is
significantly larger than what was measured and calculated for
small nickel clusters in [35–37]. The magnetism from the atom to
the bulk in nickel clusters was studied by measuring the clusters
deflections of a molecular beam in an inhomogeneous magnetic
field in [35] and the measurements were improved in [36].
According to [36], the spontaneous moment per atom decreases
from 1.8 to 0:68mB with increasing the atom number per cluster
from 5 to 740, showing a tendency of further decrease at even
Fig. 8. Spontaneous magnetization Ms as a function of temperature T. Symbols are
for the nickel nanoparticles obtained from model fits in Fig. 4(a) and (b) and solid
line is for the bulk nickel calculated from Eq. (13).

3840
D.-X. Chen et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3834–3840
larger atom numbers. The variation up to a cluster of 60 atoms
was explained by calculating the spin-polarized electronic
structure with a self-consistent tight-binding method considering
3d, 4s, and 4p valence electrons [37]. The core of our nickel
with previous calculations on nickel clusters. Nevertheless, if the
core and the shell may be regarded as ferromagnetic and
antiferromagnetic, respectively, then the difficulty of over-large
Ms in the core may be overcome by considering the exchange
interaction between the core and the shell.
particles of diameter D0ꢀ2
d
¼ 5:6 nm contains about 104 atoms,
which is one order of magnitude more than the upper limit
studied in [35,36], and corresponds to a moment of 1:04mB per
atom. This over-large Ms in the core might be related to the
difference in atomic structure; the clusters have quite different
structures from fcc as in our case. But more reasonably, the
resultant over-large Ms in the core may be a consequence of
interaction between the core and the shell, which is not
considered in our core–shell model.
Acknowledgments
We are grateful to D. Givord for his valuable comments. Partial
financial support from the Ministerio de Cıencia e Innovacion
(MAT2009-08024 and CONSOLIDER-NANOSELECT-CSD2007-
00041), the Generalitat de Catalunya (2009SGR203 and FI Grant
of OP), and the CSIC (CRIMAFOT-PIF08-016) is acknowledged.
´
The large Ms variation in ferromagnetic nanoparticles is a new
phenomenon that has to be properly explained. Its explanation
turns out to be difficult, since unlike the case of ferrites whose
magnetic ordering occurs among 3d electrons localized in each
iron ion, the band theory explaining magnetic ordering of
ferromagnets itself is defined for the whole body with ignored
local variation of magnetization. The spherical particles consisting
of few cubic crystallites suggest the existence of a spherical
amorphous shell containing oxygen atoms with an antiferromag-
netic properties. If this is true, the discovered magnetic core–shell
structure would be directly linked to a core–shell microstructure,
and the magnetization rotations in the core would not only be
driven by the applied field but also be impeded by an opposite
exchange field owing to the exchange interaction between the
ferromagnetic core and the antiferromagnetic shell. As a result,
the low-field susceptibility of the assembly should be reduced
from what is calculated from the Langevin function without
considering the core–shell interaction. If the exchange field is
relatively larger for smaller particles than for larger particles, then
smaller particles contribute to the reduction of susceptibility
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A core–shell model developed for the study of ferrimagnetic
oxide nanoparticles is used for metallic ferromagnets. Values of
Ms in the core larger than its bulk value may result from the
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